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ST429 – Statistical Methods for Risk Management

Green finance

Deadline: Friday 6th of January 2023 at 17:00 (UK time)

A.  Read me

• Group project. This submission will be strictly done in groups of min- imum 3 people and maximum 4 people.  Only one submission per group should be uploaded. Each group will have a group num- ber assigned to them. The numbers for each group will be assigned in an excel sheet shared with everyone.

Files to be submitted. Three files will be submitted:

1. Project as a PDF file: Include your results and code.

2. Code as an R file (or .Rmd): the R code must be submitted as a separated file to compile your results.  The code in the PDF file and the R code in a separate file must be the same.

3. Data in an excel or text file: the data you call in your code.

• Submission. A portal for submission will be open on Moodle towards the deadline. The names of the files to be uploaded should contain your group number as indicated in the examples here. For example: If your group is number 3, name your PDF file:  ST429_project_group3.pdf; and name your R file: ST429_code_group3.R. The name of the data

is up to you.

• Project file organisation.  You are encouraged to write your project using LATEX. All the written content must be typed. You may structure your project as follows:

1. Cover: Group number, candidate numbers (no names).

2. Introduction

3. Results

4. Conclusions

5. References

6. Appendix: R code and other content you find necessary to include

• R file organisation.  Your code, that is also attached above, should have all necessary comments to follow the computations and results given.  Comment which participants (using candidate numbers only, no names) contributed in what parts of the code.  Set a seed before your simulations if any.

• Length of the project: The project in PDF should have around 18 pages (without R code attached). Use font size 11pt or 12pt.

• Assessment.   The project will be graded over  100 marks with 25% weight in your final grade.

• Plagiarism.

“All work for classes and seminars as well as scripts must be the stu- dent’s own work. Quotations must be placed properly within quotation marks or indented and must be cited fully.  All paraphrased material must be acknowledged. Infringing upon this requirement, whether de- liberately or not, or passing of the work of others as the work of the student, whether deliberately or not, is plagiarism.”

Note that all reports will be submitted to Turnitin for textual similarity review and the detection of plagiarism.

• Penalty for late submission. Please be aware of the School’s penalties for late submission of coursework:

“Five marks out of 100 will be deducted for coursework submitted within 12 hours of the deadline and a further five marks will be deducted

for submissions made in the next 12 hours, making a total of 10 marks for the first 24 hours. Five marks will be deducted for each subsequent 24-hour period (not limited to working days, i.e:  including weekends and closure periods) until the coursework is submitted. ”

• Final remarks.  For the cover, please indicate the group number and the candidate numbers of students that contributed in the coursework.

B.  Project

In December 2015, 195 countries signed the Paris Agreement to reduce the risk of climate change. According to this agreement, the different countries compromised to control and limit the release of greenhouse gases. However, a clear plan on how to reduce emissions was not set and couple of years later there was no proof that countries were meeting the goals of the agreement. Nowadays, the pandemic stressed the importance of climate risk and the need to look for sustainable solutions in different sectors.  Currently, The 2022 United Nations Climate Change Conference (COP27) is taking place. The purpose of this project is inspired by the following article

Bloomberg: Action 91

Find more actions points here

Bloomberg Actions

Students will study stock prices from similar companies to the ones la- belled as leaders and laggards, in the article.  For the data you download, make sure you include some stocks related to both sides. The article above should give you an idea of what stocks to look at.

Some of the following instructions are intentionally vague and open ended, they may not have universal correct answers. I am giving you some guidelines for each step of the project, but you may want to add more results related to the topics we covered in class to address the following items.

1. Download 10 different daily stock prices.  The data should be recent and go back in time at least to 2016 (example: from January 2016 to October 2022). You can find historic data in  Wharton Research Data Services or  Yahoo Finance  (this option will be faster).  Prepare the data so that it can be analysed by R.

2. Analyse the log returns of the assets in your portfolio.  Comment on what happened for these stock prices. Can you find any special events?

3. Construct a loss random variable associated to your portfolio with an initial investment V0  > 0. Consider only positive random losses of your portfolio and fit a Pareto distribution to large losses L|L > m, where m is a value of your choice.  A common choice for m is the empirical quantile at α, where α ∈ (0, 1). Discuss your choice of m and calculate capital requirements with VaR and ES at different confidence levels for L|L > m.  Compare your results assuming the a Pareto distribution and the empirical distribution. Discuss your results.

4. Take each stock as an individual investment and analyse the depen- dence structure of the different risks (minus log-returns).  Among the copulas we learned in class, which copula fits the best to different pairs? (You may want to fit many pairs, but include detailed information of pairs that you consider interesting, more results can be included in ta- bles).  Explain all the steps of your fitting, comment on the choices of initial parameters.  Support your results with different measures of dependence.

5. Previously, you fitted a copula to pairs of losses, say (L1 , L2 )\  ∼ C , then we can estimate a joint model for (L1 , L2 )\ . For a relevant pair, test the bivariate model, and simulate (L1 , L2 ).  Using this joint distribution, estimate the Expected Shortfall of the aggregated losses ESα (L1 + L2 ) at different levels. Compare these values if the pair (L1 , L2 ) has instead a Gaussian copula and Gumbel copulas with parameters θ → ∞ .

6. Construct a Principal component analysis and choose the first compo- nent as an index.  Find the dependence structure between this index to the stock with the most relevant presence in the second component. Among the copulas we learned in class, which copula best fits the ob- servations?